5. Bayes' Rule (15 marks). Suppose that there are two urns, i = A, B, and one is chosen randomly by nature. Urn A has 3 red and 6 black balls. Urn B has 6 red and 3 black balls. It is common knowledge that nature chooses each urn with probability 0.5. A sequence of three balls is drawn with replacement from one of the urns. Experimental subjects do not know which urn the balls are drawn from. Let x denote the number of red balls that come up in the sample of 3 balls, x = 0,1,2,3. Suppose that the sample, based on three draws, turns out to be x = 2. (a) What is the posterior probability that the sample came from urn B? (10 marks) (b) How can you identify an individual who uses the representativeness heuristic to answer this question? Explain. (5 marks).